Functions and graphsAdditional / Further Maths

Reading a function value from a graph

Start at the input on the horizontal axis, find the curve, then read the output on the vertical axis.

  • The horizontal coordinate is the input. The vertical coordinate is the output.
  • Check the scale on both axes before reading a value.
  • To find , move vertically from to the curve, then horizontally to the output axis.

Example 1

Trace input 2 to the curve

Read the requested value from the graph. Each grid step is one unit. The marked point has input 2 and output 3.

Graph of f(x) = x squared minus 1, with the point (2, 3) marked.−4−3−2−101234−4−3−2−1123456(2, 3)

Example 2

Find the input when . Read across from 3 on the -axis, then down to the -axis.

Graph of f(x) = 1 minus x, with the point (-2, 3) marked.−4−3−2−101234−4−3−2−1123456(−2, 3)

Your turn

Question 1

Read from the graph. Each grid step is one unit.

Graph of f(x) = x**2 - 1. Each grid step represents one unit.−4−3−2−101234−4−3−2−1123456
Check answer
Question 2

Read from the graph. Each grid step is one unit.

Graph of f(x) = 2*x + 1. Each grid step represents one unit.−4−3−2−101234−4−3−2−1123456
Check answer
Question 3

Read from the graph. Each grid step is one unit.

Graph of f(x) = 4 - x. Each grid step represents one unit.−4−3−2−101234−4−3−2−1123456
Check answer
Question 4

Read from the graph. Each grid step is one unit.

Graph of f(x) = 4 - x**2. Each grid step represents one unit.−4−3−2−101234−4−3−2−1123456
Check answer
Question 5

Read from the graph. Each grid step is one unit.

Graph of f(x) = x**2 - 2. Each grid step represents one unit.−4−3−2−101234−4−3−2−1123456
Check answer
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